{"id":585,"date":"2025-04-01T14:26:21","date_gmt":"2025-04-01T06:26:21","guid":{"rendered":"http:\/\/106.12.148.75\/?p=585"},"modified":"2025-05-20T21:03:03","modified_gmt":"2025-05-20T13:03:03","slug":"differentiable-mpc-for-end-to-end-planning-and-control","status":"publish","type":"post","link":"https:\/\/jamilblog.top\/?p=585","title":{"rendered":"Differentiable MPC for End-to-end Planning and Control"},"content":{"rendered":"\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"http:\/\/106.12.148.75\/wp-content\/uploads\/2025\/04\/1743488730-Differentiable-MPC-for-End-to-end-Planning-and-Control.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"\u5d4c\u5165 Differentiable MPC for End-to-end Planning and Control\"><\/object><a id=\"wp-block-file--media-d320a2ba-55db-4eb6-9fbd-2f086a857027\" href=\"http:\/\/106.12.148.75\/wp-content\/uploads\/2025\/04\/1743488730-Differentiable-MPC-for-End-to-end-Planning-and-Control.pdf\" target=\"_blank\"  rel=\"nofollow\" >Differentiable MPC for End-to-end Planning and Control<\/a><a href=\"http:\/\/106.12.148.75\/wp-content\/uploads\/2025\/04\/1743488730-Differentiable-MPC-for-End-to-end-Planning-and-Control.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-d320a2ba-55db-4eb6-9fbd-2f086a857027\" target=\"_blank\"  rel=\"nofollow\" >\u4e0b\u8f7d<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u603b\u4f53\u601d\u8def<\/h2>\n\n\n\n<p>\u8bba\u6587\u603b\u4f53\u601d\u8def\u5229\u7528\u6c42\u89e3\u62c9\u683c\u6717\u65e5\u65b9\u7a0b\uff0c\u5c06\u7ea6\u675f\u95ee\u9898\u8f6c\u6362\u4e3a\u65e0\u7ea6\u675f\u95ee\u9898\uff0c\u5e76\u901a\u8fc7\u6784\u5efa\u7684kkt\u6761\u4ef6\u501f\u52a9\u5bf9\u6700\u4f18\u89e3\u7684\u5bfc\u6570\u6765\u9690\u5f0f\u7684\u6c42\u89e3\u6240\u6d89\u53ca\u7684loss\u5bf9\u53c2\u6570\uff08C\uff0cc\uff0cF\uff0cf\uff09\u7684\u5bfc\u6570\uff0c\u8fd9\u5176\u4e2d\u6e17\u900f\u53c2\u6742\u8fd9\u8bb8\u591a\u5f15\u7406\uff0c\u5982\u679c\u53ea\u662f\u4f7f\u7528\u53ef\u4ee5\u4e0d\u6c42\u751a\u89e3\uff0c\u66f4\u591a\u7ec6\u8282\u9700\u8981\u4ed4\u7ec6\u63a8\u6572<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7b97\u6cd5\u6d41\u7a0b<\/h2>\n\n\n\n<p><\/p>\n\n\n\n<p><strong># **1. \u7b97\u6cd5\u6d41\u7a0b\uff08Algorithm 2\u7b80\u5316\u7248\uff09**<\/strong><\/p>\n\n\n\n<p>\u2022 <strong>**\u8f93\u5165**<\/strong>\uff1a\u521d\u59cb\u72b6\u6001$x_{\\text{init}}$\uff0c\u521d\u59cb\u63a7\u5236\u5e8f\u5217$u_{\\text{init}}$\uff0c\u53c2\u6570$\\theta$\u3002<\/p>\n\n\n\n<p>\u2022 <strong>**\u524d\u5411\u4f20\u64ad**<\/strong>\uff1a<\/p>\n\n\n\n<p>1. \u4f7f\u7528iLQR\u6c42\u89e3MPC\uff0c\u5f97\u5230$\\tau^*$\u3002<\/p>\n\n\n\n<p>2. \u8bb0\u5f55\u6700\u540e\u4e00\u6b21\u8fed\u4ee3\u7684$H^n$\uff08\u6210\u672cHessian\uff09\u548c$F^n$\uff08\u52a8\u529b\u5b66Jacobian\uff09\u3002<\/p>\n\n\n\n<p>\u2022 <strong>**\u53cd\u5411\u4f20\u64ad**<\/strong>\uff1a<\/p>\n\n\n\n<p>1. <strong>**\u6784\u9020\u96f6\u7ea6\u675fLQR\u95ee\u9898**<\/strong>\uff1a<\/p>\n\n\n\n<p>\u25e6 \u6210\u672c\u51fd\u6570\uff1a$\\sum_t \\frac{1}{2} d_{\\tau_t}^\\top H^n d_{\\tau_t} + (\\nabla_{\\tau_t^*}\\ell)^\\top d_{\\tau_t}$\u3002<\/p>\n\n\n\n<p>\u25e6 \u7ea6\u675f\uff1a$d_{x_1}=0$\uff0c$d_{x_{t+1}}=F^n d_{\\tau_t}$\uff0c$d_{u_{t,i}}=0$\uff08\u82e5$u_{t,i}^*$\u5728\u8fb9\u754c\uff09\u3002<\/p>\n\n\n\n<p>2. <strong>**\u6c42\u89e3\u5f97\u5230<\/strong><strong>$<\/strong><strong>d_\\<\/strong><strong>tau<\/strong><strong>^*<\/strong><strong>$<\/strong><strong>**<\/strong>\uff1a\u590d\u7528\u524d\u5411\u4f20\u64ad\u7684\u77e9\u9635\u5206\u89e3\uff0c\u9ad8\u6548\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p>3. <strong>**\u8ba1\u7b97\u68af\u5ea6**<\/strong>\uff1a\u5229\u7528\u516c\u5f0f8\u548c\u94fe\u5f0f\u6cd5\u5219\u66f4\u65b0$\\theta$\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u603b\u4f53\u601d\u8def \u8bba\u6587\u603b\u4f53\u601d\u8def\u5229\u7528\u6c42\u89e3\u62c9\u683c\u6717\u65e5\u65b9\u7a0b\uff0c\u5c06\u7ea6\u675f\u95ee\u9898\u8f6c\u6362\u4e3a\u65e0\u7ea6\u675f\u95ee\u9898\uff0c\u5e76\u901a\u8fc7\u6784\u5efa\u7684kkt\u6761\u4ef6\u501f\u52a9\u5bf9\u6700\u4f18\u89e3\u7684\u5bfc\u6570\u6765\u9690\u5f0f\u7684\u6c42\u89e3\u6240\u6d89\u53ca &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[12,3],"tags":[47,48,45,46,36,37],"class_list":{"0":"post-585","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"hentry","6":"category-12","7":"category-planning","8":"tag-mpc","10":"tag-45","11":"tag-46","12":"tag-36","13":"tag-37"},"_links":{"self":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=585"}],"version-history":[{"count":4,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/585\/revisions"}],"predecessor-version":[{"id":595,"href":"https:\/\/jamilblog.top\/index.php?rest_route=\/wp\/v2\/posts\/585\/revisions\/595"}],"wp:attachment":[{"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jamilblog.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}